On Wed, 07 Feb 2007 22:50:01 -0700, Luis Finotti <[EMAIL PROTECTED]> wrote: > I wanted to make a little script that given an elliptic curve and two > points, it would plot the addition with the corresponding lines, > labels, etc. to use in a talk for undergraduates. > > I wanted to only specify the x-coordinates and choices for the > corresponding y's (the larger value, or the smaller), and have the > script compute the exact value for the y's. Since I would be > plotting, I was working over the reals. The problem is that the > approximations do not allow me to define points on the curve, I think > due to imprecision. More precisely: > > > > sage: E=EllipticCurve(RR,[0,-1]) > sage: x0=RR(4)^(1/3) > sage: y0=sqrt(RR(3)) > sage: E([x0,y0])
> I can implement the addition formula and work with the approximations > instead of using Sage to add the points (or call Pari, which I think > does it), but I thought I should see if I am missing something and/or > if this is the expected behavior. It's good that you asked. Do this instead: sage: E=EllipticCurve(RR,[0,-1]) sage: x0=RR(4)^(1/3) sage: y0=sqrt(RR(3)) sage: p=E.point([x0,y0,1], check=False) sage: p (1.58740105196819 : 1.73205080756887 : 1) sage: 2*p, 3*p ((1.58740105196819 : -1.73205080756887 : 1), (0.000000000000000 : 1.00000000000000 : 0.000000000000000)) NOTE: It's important to input [x0,y0,1], i.e., a 3-tuple, since check=False really does no checking about the input, and you'll get surprising failures later if you're not careful. William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
